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Single Idea 19057
[filed under theme 5. Theory of Logic / G. Quantification / 1. Quantification
]
Full Idea
Classical quantification represents an infinite conjunction or disjunction, and the truth-value is determined by the infinite sum or product of the instances ....but this presupposes that all the instances already possess determinate truth-values.
Gist of Idea
Classical quantification is an infinite conjunction or disjunction - but you may not know all the instances
Source
Michael Dummett (The philosophical basis of intuitionist logic [1973], p.246)
Book Ref
Dummett,Michael: 'Truth and Other Enigmas' [Duckworth 1978], p.246
A Reaction
In the case of the universal quantifier, Dummett is doing no more than citing the classic empiricism objection to induction - that you can't make the universal claim if you don't know all the instances. The claim is still meaningful, though.
The
23 ideas
with the same theme
[general ideas about expressing quantities of objects]:
11149
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Affirming/denying sentences are universal, particular, or indeterminate
[Aristotle]
|
9106
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The word 'every' only signifies when added to a term such as 'man', referring to all men
[William of Ockham]
|
9950
|
A quantifier is a second-level predicate (which explains how it contributes to truth-conditions)
[Frege, by George/Velleman]
|
14137
|
'Any' is better than 'all' where infinite classes are concerned
[Russell]
|
9467
|
Wittgenstein tried unsuccessfully to reduce quantifiers to conjunctions and disjunctions
[Wittgenstein, by Jacquette]
|
10922
|
Objects are the values of variables, so a referentially opaque context cannot be quantified into
[Quine]
|
9015
|
Universal quantification is widespread, but it is definable in terms of existential quantification
[Quine]
|
10926
|
Quantifying into referentially opaque contexts often produces nonsense
[Quine]
|
10311
|
No sense can be made of quantification into opaque contexts
[Quine, by Hale]
|
10538
|
Finite quantification can be eliminated in favour of disjunction and conjunction
[Quine, by Dummett]
|
10799
|
Nominalists should quantify existentially at first-order, and substitutionally when higher
[Marcus (Barcan)]
|
15891
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Traditional quantifiers combine ordinary language generality and ontology assumptions
[Harré]
|
19057
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Classical quantification is an infinite conjunction or disjunction - but you may not know all the instances
[Dummett]
|
13438
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'Prenex normal form' is all quantifiers at the beginning, out of the scope of truth-functors
[Bostock]
|
6042
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The quantifier is overrated as an analytical tool
[McGinn]
|
6067
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Existential quantifiers just express the quantity of things, leaving existence to the predicate 'exists'
[McGinn]
|
6890
|
Quantifiers turn an open sentence into one to which a truth-value can be assigned
[Mautner]
|
18492
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Not all quantification is either objectual or substitutional
[Williamson]
|
11007
|
Quantifiers are second-order predicates
[Read]
|
8452
|
Traditionally, universal sentences had existential import, but were later treated as conditional claims
[Orenstein]
|
16416
|
The quantifier in logic is not like the ordinary English one (which has empty names, non-denoting terms etc)
[Hofweber]
|
21643
|
The inferential quantifier focuses on truth; the domain quantifier focuses on reality
[Hofweber]
|
23494
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Conjunctive and disjunctive quantifiers are too specific, and are confined to the finite
[Morris,M]
|